Question

The function f(x) varies inversely with x and f(x)= -10 when x = 20

What is the inverse variation equation?
A. f(x) = -2/x
B. f(x) = - 50/x
C. f(x) = - 0.5/x
D. f(x) = -5/x

Answer 1

The inverse variation function can be written as:

`f(x)=(-200)/(x)`

Explanation:

Given :

`f(x)` varies inversely with
`x`

when
`x=20`,
`f(x)=-10`

To find the inverse variation equation.

Solution:

`f(x)` varies inversely with
`x` can be represented as:

`f(x)` ∝
`(1)/(x)`

Thus,
`f(x)=(k)/(x)`

where
`k` represents the constant of proportionality.

We can determine the value of
`k` by plugging in the values given.

when
`x=20`,
`f(x)=-10`

So, we have

`-10=(k)/(20)`

Multiplying both sides by 20.

`20* (-10)=20* (k)/(20)`

`-200=k`

Thus the inverse variation function can be written as:

`f(x)=(-200)/(x)`